Method for carbon dioxide sequestration

ABSTRACT

A method for geo-sequestration of a carbon dioxide includes selection of a target water-laden geological formation with low-permeability interbeds, providing an injection well into the formation and injecting supercritical carbon dioxide (SC—CO 2 ) into the injection well under conditions of temperature, pressure and density selected to cause the fluid to enter the formation and splinter and/or form immobilized ganglia within the formation. This process allows for the immobilization of the injected SC—CO 2  for very long times. The dispersal of scCO2 into small ganglia is accomplished by alternating injection of SC—CO 2  and water. The injection rate is required to be high enough to ensure the SC—CO 2  at the advancing front to be broken into pieces and small enough for immobilization through viscous instability.

RELATED APPLICATIONS

This invention claims the benefit of U.S. Patent Application Nos.61/675,677 filed on Jul. 25, 2012, entitled “Ganglion Dynamics and itsImplications to Geologic Carbon Dioxide Storage”, the contents of whichare herein incorporated by reference in their entirety.

GOVERNMENT RIGHTS

The Government has rights to this invention pursuant to Contract No.DE-AC04-94AL85000 awarded by the U.S. Department of Energy.

FIELD

The invention relates generally to a method of sequestering carbondioxide in a geologic formation, and more particularly to immobilizinginjected supercritical CO₂ (SC—CO₂) by forming scCO₂ ganglia in theformation through viscous instability.

BACKGROUND OF THE INVENTION

Human activities have an impact upon the levels of greenhouse gases inthe atmosphere, which in turn is believed to affect the world's climate.Changes in atmospheric concentrations of greenhouse gases have theeffect of altering the energy balance of the climate system andincreases in anthropogenic greenhouse gas concentrations are likely tohave caused most of the increases in global average temperatures sincethe mid-20th century. Earth's most abundant greenhouse gases includecarbon dioxide, methane, nitrous oxide, ozone and chlorofluorocarbons.The most abundantly-produced of these by human industrial activity isCO₂.

Various strategies have been conceived for permanent storage of CO₂.These strategies include sequestration of gases in various deepgeological formations (including saline aquifers and exhausted gasfields), liquid storage in the ocean, and solid storage by reaction ofCO₂ with metal oxides to produce stable carbonates.

The most promising of these strategies is sequestration in geologicalformations. In these strategies, CO₂, generally in supercritical (SC)form, is injected directly into underground geological formations. Oilfields, gas fields, saline aquifers, un-minable coal seams, andsaline-filled basalt formations have been suggested as storage sites.Various physical (e.g., highly impermeable cap-rock), solubility andgeochemical trapping mechanisms are generally expected to prevent theCO₂ from escaping to the surface. Geo-sequestration can also beperformed for other suitable gases.

Saline aquifers contain highly mineralized brines, and have so far beenconsidered of little benefit to humans. Saline aquifers have been usedfor storage of chemical waste in a few cases, and attempts have beenmade to use such aquifers to sequester CO₂. The main advantage of salineaquifers is their large potential storage volume and their commonoccurrence. One disadvantage of any practical use of saline aquifers forthis purpose is that relatively little is known about them. Leakage ofCO₂ back into the atmosphere has been considered a potential problem insaline aquifer storage.

The densest concentration of CO₂ that can be placed in a porousformation such as a saline aquifer is when CO₂ is in a supercriticalstate—referred to herein as SC—CO₂. Most sequestration schemes are basedon injection of SC—CO₂ in this supercritical state when the materialbehaves as a relatively dense compressible liquid with an extremely lowviscosity, far lower than any formation liquid. The object is todisplace most or all of the water in the saline aquifer, replacing 100%or some fraction of the porosity with SC—CO₂.

Injection of gaseous CO₂ (i.e. not in supercritical form) into asubsurface formation in solution with water at the maximum solubilitylimit is another approach to sequestration of this gas that has beenproposed with mixed success in the past. Prior to the present invention,a problem of sequestering of CO₂ by dissolution in an aqueous solutionwithin geological formations has been that the porous volume of theformation is occupied far less efficiently than the occupation whichoccurs upon injection of SC—CO₂. Once the active injection phase iscompleted, there is no more active mixing within the porous medium.Thereafter, the dissolution of the CO₂ within the formation water iscontrolled by the concentration differences, the contact area, and thediffusion path length. Mass transfer rates associated with suchconcentration gradient-driven diffusion processes in porous media areslow and it is expected that thousands of years may be required toapproach full dissolution of the CO₂ in the aqueous phase within thegeological formation.

The “reduced-mixing, long-term concentration gradient diffusion” problempersists even with injection of SC—CO₂. At the high injection ratesproposed for SC—CO₂ sequestration, the SC—CO₂ will first displace waterand occupy the pore space directly, with only a small amount ofconvective and dispersive-occurring mixing at the displacement fronts.As SC—CO₂ is injected over time, a growing area of contact is generatedbetween the two fluids and a dissolution zone is generated. The SC—CO₂then becomes dissolved into the saline water along this contact area,largely as the result of diffusion and dispersion associated with forcedadvection caused by pressure driven flow (from injection of the SC—CO₂under pressure).

Because of the density difference between saline water and SC—CO₂, thereare also gravitational forces that will tend to segregate the liquids inthe saline aquifer: the SC—CO2 will rise above the denser water, forminga “pancake” under zones that are finer-grained with poorer permeability(shale streaks, siltstones, etc.). This not only suppresses part of themixing component that would arise in a more uniform displacement, italso leads to a significant inefficiency in the access to the porevolumes in the formation: portions of the formation remote from theinjection point are largely inaccessible to any storage mechanism(displacement by or dissolving of CO₂ into solution).

Once the injection ceases, only a small fraction of the SC—CO₂ has goneinto solution because of the mixing and diffusive effects at thedisplacement fronts, and because the advective driving force (injectionpressure) ceases. The CO₂ can no longer be advectively mixed with thewater, and this leaves only diffusion effects that are driven solely byconcentration gradients of CO₂ in the water.

In a saline aquifer formation, after injection, the SC—CO₂ remains highin the zone above the injection site due to its lesser density. Thisdensity-graded system provides a stabilizing force that further reducesthe rate of any diffusion process. Initially, the diffusion front isrelatively narrow and distinct with large surface area between the CO₂and water and the solution process happens relatively efficiently. Butover time this front grows and widens vertically. As a result, the frontbecomes less distinct. This produces a thicker diffusion or transitionzone with less surface area between the CO₂ and water that has a low CO₂concentration (i.e. the transition-dissolution-contact area between theSC—CO₂ and the formation water becomes enriched with CO₂. The verticaldistance between water from remote regions of the formation and SC—CO₂grows as CO₂-unsaturated water is further away from the SC—CO₂. Hencethe diffusion/solution process slows considerably. As a result it cantake many thousands of years for CO₂ to enter into solution, since insitu movement of water at remote regions of the formation (to facilitatethe CO₂ in solution with water process) is very slow. At this stage,there is no convective mixing between the SC—CO₂ and the formation waterdue to the density graded system.

These prior strategies require that the geologic formation include ahigh integrity cap rock to prevent the escape and limit the movement ofthe injected CO₂ or SC—CO₂. Residual trapping of a non-wetting liquidphase in a brine reservoir may be an important mechanism for long-termCSS. Residual trapping can potentially relax stringent requirements forthe integrity of cap rocks and allow utilization of open or dippingstructures for carbon storage.

At this time, a method for immobilizing CO₂ in geologic formationshaving questionable cap rock integrity and/or in an open or dippinggeologic formation for hundreds to millions of years has not beendeveloped.

A need remains, therefore, for a method to immobilize CO₂ in geologicformations having questionable cap rock integrity and/or in an open ordipping geologic formation for hundreds to millions of years.

SUMMARY OF THE INVENTION

An embodiment of the present disclosure is directed to a method forpredicting the movement of supercritical-carbon dioxide injected into ageologic formation. The method includes characterizing the geologicformation; determining the surface tension between fluid of the geologicsite and supercritical carbon dioxide; determining supercritical carbondioxide ganglion size for entrapment for a given fluid velocity;determining the maximum supercritical carbon dioxide ganglion formationby induced viscous interface instability; and determining the traveldistance of supercritical carbon dioxide ganglion within the geologicformation based on entrapment criteria.

Another embodiment of the present disclosure is directed to a method forstoring a carbon dioxide in a geologic formation. The method includesinjecting supercritical carbon dioxide and a fluid into the geologicformation.

Another embodiment of the present disclosure is directed to a method ofpredicting risk of release of CO2 from CO2 geologic formation storage.The method includes characterizing the geologic formation; determiningthe surface tension between fluid of the geologic site and supercriticalcarbon dioxide; determining supercritical carbon dioxide ganglion sizefor entrapment for a given fluid velocity; determining the maximumsupercritical carbon dioxide ganglion formation by induced viscousinterface instability; determining the travel distance of supercriticalcarbon dioxide ganglion within the geologic formation based onentrapment criteria: and determining the risk based on supercriticalcarbon dioxide ganglion entrapment criteria.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows a thin section of Mount Simon Sandstone showing a typicalsandstone pore structure (the horizontal field of view is 1.76 mm on theoriginal specimen).

FIG. 2 is an illustration of a conceptual model of pore structure andganglion movement with pore-scale ganglion movement at advancing andreceding fronts.

FIG. 3 shows a graph showing the relationship for critical verticaldimension for the entrapment of a SC—CO₂ ganglion as a function of porediameter and contact angle (10°, 40°, and 70°) for a buoyance-only case.The size ratio of pore to throat is set to 5:1.

FIG. 4 is a graph showing the effect of the pore size of an interbed onSC—CO₂ trapping. The ratio of pore diameter to throat diameter is 5:1for both sandstone and interbed.

FIG. 5 is graph showing the finger spacing induced as SC—CO₂ displacespore water during CO₂ injection, for two different reservoirpermeabilities. The shaded area indicates the possible range of frontvelocities, assuming a typical CO₂ injection rate of 10⁴ to 10⁶ metrictons per year in a borehole of 0.3 m diameter and with 10 m injectioninterval. Finger spacing here is equivalent to the vertical dimension ofa ganglion in FIG. 3.

FIG. 6 shows ganglion breaking and trapping due to interfaceinstability. The radii of pore throat and pore body are assumed to be0.1 and 0.5 mm, respectively. To the left of the vertical broken line,ganglia are small and trapped. To the right, ganglia are large enough toattain sufficient rising velocities to cause further breaking up andtrapping. The size of regenerated ganglia is calculated from equations(15) and (16) by setting α=0, and thus SC—CO₂ fingering due to gravityinstability is automatically accounted. Since the size of regeneratedganglia is smaller than the critical size (˜0.1 m) for mobilization, allregenerated ganglia become trapped.

FIG. 7 is a graph showing mobilization and entrainment of ganglia byflow field. Larger ganglia would be more easily mobilized and movefaster than the smaller ones in a given flow field. The radii of porethroat and pore body are assumed to be 0.1 and 0.5 mm, respectively.

FIG. 8 is an illustration of the existence of an optimal condition forSC—CO₂ capillary trapping.

FIG. 9 is an illustration of an embodiment of an injection fieldaccording to the present disclosure. 12

FIG. 10 is a flow chart of an exemplary embodiment of a method ofpredicting long term risk of storing CO₂ in a geologic formationaccording to the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present disclosure is directed to a method of sequestering orstoring CO₂ in a geologic formation. The CO₂ injected by the disclosedmethod creates ganglia or small pockets of CO₂ that are immobilized bycapillary tapping. Capillary trapping of CO₂ and SC—CO₂ significantlyexpands storage capacity through efficient utilization of subsurfacereservoirs. The disclosed mechanism relaxes the need for stringentrequirements for the integrity of cap rocks for CO₂ storage andtherefore can significantly enhance storage capacity and security.

The present disclosure is further directed to a method that usesganglion dynamics to predict the capillary trapping of supercritical CO2(SC—CO₂) under relevant reservoir conditions. The disclosed methodinjects SC—CO₂ under conditions that break the injected SC—CO₂ intosmall disconnected ganglia, which enhances the efficiency of capillarytrapping since the mobility of a ganglion is inversely dependent on itssize. SC—CO₂ ganglia can be engineered by promoting CO₂-water interfaceinstability during immiscible displacement, and their size distributioncan be controlled by an injection mode utilizing water-alternating-gasand/or gas/fluid mixtures and rate. The disclosed method can also beused to break large mobile ganglion into smaller ganglia due toCO₂-brine interface instability during buoyant rise, thus becoming lessmobile. The mobility of SC—CO₂ in the subsurface is thereforeself-limited. Vertical structural heterogeneity within a reservoir caninhibit the buoyant rise of SC—CO₂ ganglia. The dynamics of SC—CO₂ganglia described here provides a new perspective for the security andmonitoring of subsurface CO₂ storage.

According to an embodiment of the disclosure, a method utilizing a modelis disclosed that uses the theory of ganglion dynamics to predict themobility of SC—CO₂ injected into a water-wet subsurface porous medium.The porous medium may be a sandstone reservoir. According to thisembodiment, it can be predicted that the entrapment of SC—CO₂ ganglia insubsurface environments is improved by breaking up the injected SC—CO₂into small blobs that enhance capillary entrapment.

The model assumes that the flow of both SC—CO2 inside a ganglion andwater outside follows Darcy's law:

$\begin{matrix}{{\overset{harpoonup}{V}}_{s} = {{- \frac{k}{\mu_{s}}}{\overset{harpoonup}{\Delta}( {P_{S} + {\rho_{S}{gz}}} )}}} & (1) \\{{\overset{harpoonup}{V}}_{w} = {{- \frac{k}{\mu_{w}}}{\overset{harpoonup}{\Delta}( {P_{W} + {\rho_{W}{gz}}} )}}} & (2) \\{{\overset{harpoonup}{\Delta} \cdot {\overset{harpoonup}{V}}_{s}} = {{\overset{harpoonup}{\Delta} \cdot {\overset{harpoonup}{\Delta}}_{w}} = 0}} & (3)\end{matrix}$

where

and

are the velocity fields of SC—CO₂ and water, respectively; k is thepermeability of the porous medium; μ_(s) and μ_(w) are the viscosity ofSC—CO₂ and water, respectively; ρ_(s) and ρ_(w) are the density ofSC—CO₂ and water, respectively; g is the gravitation acceleration; P_(s)and P_(w) are the pressures of SC—CO₂ and water, respectively; and z isthe vertical coordinate pointing upward.

At the macroscopic scCO2-water interface:

$\begin{matrix}{{{\overset{harpoonup}{V}}_{s} \cdot \overset{harpoonup}{n}} = {{\overset{harpoonup}{V}}_{w} \cdot \overset{harpoonup}{n}}} & (4) \\{{P_{s} - P_{w}} = {{\sigma*{\overset{harpoonup}{\nabla}{\cdot \overset{harpoonup}{n}}}} + P_{c}}} & (5) \\{P_{c} = \{ \begin{matrix}\frac{2\;\sigma\;{\cos(\theta)}}{r_{n}} & {{at}\mspace{14mu}{an}\mspace{14mu}{advancing}\mspace{14mu}{front}} \\\frac{2\sigma\;{\cos(\theta)}}{r_{p}} & {{at}\mspace{14mu} a\mspace{14mu}{receding}\mspace{14mu}{front}}\end{matrix} } & (6)\end{matrix}$

where

is the normal unit vector of the macroscopic ganglion surface pointingfrom SC—CO₂ to water; σ is the pore-scale surface tension between SC—CO₂and water; P_(c) is the pore-scale capillary pressure; θ is the contactangle between the SC—CO₂-water interface and the underlying solidsurface; r_(n) and r_(p) are the effective radii of pore throat and porebody, respectively; and σ* is the effective macroscopic surface tensionbetween SC—CO₂ and water—an empirical parameter to capture the effect ofsurface tension on the stability of macroscopic SC—CO₂-water interface.

FIG. 1 illustrates a typical pore structure in sandstone. As can be seenin FIG. 1, the pore structure is characterized by the sizes of pore bodyand pore throat. Sandstone grains 10 are surrounded by pore space 20.The non-wetting SC—CO₂ phase tends to occupy large pore spaces as muchas possible to minimize interfacial energy. A ganglion of SC—CO2occupies multiple pores. A movement of a ganglion needs to overcome thecapillary pressure difference between the advancing the receding fronts.

FIG. 2 illustrates the inverse relationship between capillary pressureand radius of pore throat at the advancing front and capillary pressureand radius of pore body at the receding front as captured in equation(6). For simplicity, it is assumed that both advancing and recedingcontact angles are similar. Parameter σ* is scale-dependent and can berelated to a by accounting for surface roughness:σ*=Cσ  (7)

with C=b(d)^(1-D), where b is the fractal coefficient, d is themicroscopic investigation scale, and D is the fractal dimension of theinterface. It is assumed that both water and SC—CO₂ are non-compressible(Eq. 3). Equation (4) imposes velocity continuity across the interfacefor the normal component. Equation (5) accounts for the pressure dropacross the macroscopic SC—CO₂-water interface²², including both theeffect of macro-scale surface tension σ*, which tends to minimize themacroscopic surface area of a ganglion, and the effect of pore-scalecapillarity, which tends to impede a scCO₂ blob snapping through porethroats.

Let F(x,y,z,t)=0 denote the macroscopic surface of a ganglion. Themotion of the surface is related to the flow field by a kinematicequation:

$\begin{matrix}{{{{\overset{harpoonup}{V}}_{s} \cdot {\overset{harpoonup}{\nabla}F}} + \frac{\partial F}{\partial t}} = 0} & (8)\end{matrix}$

where t is the time. The normal unit vector

can then be calculated by:

$\begin{matrix}{\overset{harpoonup}{n} = \frac{\overset{harpoonup}{\nabla}\; F}{{\overset{harpoonup}{\nabla}F}}} & (9)\end{matrix}$

Equations 1-9 constitute a moving boundary problem for the evolution ofa scCO₂ ganglion in a porous medium. With appropriate boundary andinitial conditions, this set of equations can be solved for the motionand morphological evolution (

_(s), F) of a single ganglion or multiple ganglia.

By integrating equation (5) for the force acting over the surface of amoving ganglion, using Stokes's theorem, we obtain:

$\begin{matrix}{{∯{( {{\sigma*{\overset{harpoonup}{\nabla}{\cdot \overset{harpoonup}{n}}}} + P_{c}} ){\mathbb{d}\overset{harpoonup}{S}}}} = {{∯{( {P_{S} - P_{W}} ){\mathbb{d}\overset{harpoonup}{S}}}} = {{\int{\int{\int{{\overset{harpoonup}{\nabla}{\cdot ( {P_{S} - P_{W}} )}}{\mathbb{d}V}}}}} = {{{\Delta\rho}\;{gV}\overset{harpoonup}{z}} + {\int{\int{\int{( {{\frac{\mu_{w}}{k}{\overset{harpoonup}{V}}_{w}} - {\frac{\mu_{s}}{k}{\overset{harpoonup}{V}}_{s}}} ){\mathbb{d}V}}}}}}}}} & (10)\end{matrix}$

where Δρ=ρ_(w)−ρ_(s); V is the volume of the ganglion;

is the vertical unit vector; and S is the surface area of the ganglion.The first term on the far right hand side represents the buoyancy forcedue to the density difference between water and scCO₂; the second andthird terms, within the integral, account for the force exerted bygroundwater pressure gradient (it is assumed that the flow field ofwater can be extended to the inside of the ganglion) and for theresistance which the ganglion has to overcome in order to move throughthe porous medium. An exact evaluation of equation (10) would require afull solution of equations (1-9) for the flow fields. For simplicity, wemake the following approximations:

$\begin{matrix}{{∯{( {{\sigma*{\overset{harpoonup}{\nabla}{\cdot \overset{harpoonup}{n}}}} + P_{c}} ){\mathbb{d}\overset{harpoonup}{S}}}} \approx {{{\Delta\rho}\;{gV}\overset{harpoonup}{z}} + {( {{\frac{\mu_{w}}{k}{\overset{harpoonup}{V}}_{w}^{0}} - {\frac{\mu_{s} + {f\;\mu_{w}}}{k}{\overset{harpoonup}{V}}_{s}^{g}}} )V}}} & (11)\end{matrix}$

where

is the average velocity of groundwater flow around the ganglion; and

is the velocity of ganglion movement as a whole. During movement, waterwill be displaced around the ganglion, moving from its advancing frontto its tail at the same speed as the ganglion is advancing. This effectis captured by an effective viscosity μ_(s)+fμ_(w) in equation (11),where f is the ratio of the travel distance of water to the distance ofganglion movement. Since the water moves around the ganglion surface, fis expected to be slightly larger than 1. As a first orderapproximation, we set f equal to 1.

Let

denote the unit vector of net driving force for ganglion movement

$( {{\Delta\;\rho\;{gV}\overset{harpoonup}{z}} + {\frac{\mu_{w}}{k}V{\overset{harpoonup}{V}}_{w}^{0}}} ).$By setting

to zero, from equation (11), the entrapment criterion for a ganglion isdescribed by:

$\begin{matrix}{{{{{\Delta\rho}\;{gV}\overset{harpoonup}{z}} + {\frac{\mu_{w}}{k}V{\overset{harpoonup}{V}}_{w}^{0}}}} \leq {∯{( {{\sigma*{\overset{harpoonup}{\nabla}{\cdot \overset{harpoonup}{n}}}} + P_{c}} ){\overset{harpoonup}{l} \cdot {\mathbb{d}\overset{harpoonup}{S}}}}}} & (12)\end{matrix}$

where

·d

≧0 indicates an advancing front, and

·d

<0 indicates a receding front. The left hand side of the equationrepresents the total driving force contributed both by buoyancy andwater flow, while the right hand side is the total impedance that needsto be overcome for a ganglion to be mobilized. For a no-flow(buoyancy-only) case, the trapping criterion becomes:ΔμgV≦

(σ*

·

+P _(c))

·d

  (13)

Equation (12) indicates that capillary trapping of a SC—CO₂ ganglion iscontrolled by the pore-scale capillarity, the macro-scale surfacetension, the geometry of the ganglion, and the water flow field.Generally, the curvature of a macroscopic water-SC—CO₂ interface is muchsmaller than that of the pore-scale interface. Thus, the first term inthe integral in both equation (12) and (13) may be negligible comparedto the second term, although it may play an important role in themorphological instability of a ganglion.

First order approximation may be used to simplify the equations, inwhich a ganglion with a simple geometry is considered and the motion ofan individual ganglion is separated from its morphological instability.With the simple ganglion geometry considered below, the integration ofterm (σ*

·

) in Equations (12) and (13) vanishes. The parameter values used forthese model analyses are summarized in Table 1.

TABLE 1 List of parameter values used in the model analyses Value usedin Parameter model analyses Possible range Sources Microscopic surface0.04 N/m 0.035-0.05 N/m Refs. 35 tension of water- (pressure 8-17 and 36scCO₂ interface (σ) MPa, temperature = 40-60° C.) Scaling factor for 32-4 Ref. 21 apparent surface tension (C) Viscosity of aqueous 7.5 × 10⁻⁴N s/m² 0.4-1.0 × 10⁻³ N s/m² Ref. 9 solution (μ_(w)) Viscosity of scCO₂4.0 × 10⁻⁵ N s/m² 3.7-5.2 × 10⁻⁵ N s/m² Ref. 9 (μ_(s)) (reservoir depth= 800- 2000 m, thermal gradi- ent = 3° C./100 m) Permeability (k) 10⁻¹⁰m² 10⁻¹²-10⁻¹⁰ m² Ref. 9 Contact angle 40° 10-65° (pressure = Refs. 24between the water- 26.6-48.9 MPa, and 25 scCO₂ interface temperature =and the underlying 354.5 K) solid surface (θ) Density of scCO₂ 650 kg/m³500-700 kg/m³ for Refs. (ρ_(s)) a storage depth 37 & 38 of 0.8-2 km witha geothermal gradient of 3° C. per 100 meters) Density of aqueous 1,065kg/m³ 1,000-1,150 kg/m³ Ref. 39 solution (ρ_(w)) Gravitational 9.8 m/s²acceleration (g)

Capillary Trapping of SC—CO₂ Ganglia in the Absence of Water Flow may beapproximated. For simplicity, a vertical, cylindrical SC—CO₂ ganglionwith a height of H is considered. From equation (13), the entrapmentcondition for the ganglion is described by:

$\begin{matrix}{{H < H_{c}} = {\frac{2\;{{\sigma cos}(\theta)}}{{\Delta\rho}\; g}( {\frac{1}{r_{n}} - \frac{1}{r_{p}}} )}} & (14)\end{matrix}$

where H_(c) is the critical value of H. The contact angle between theSC—CO₂-water interface and the underlying mineral surface is animportant factor controlling the effectiveness of capillary trapping.With increasing the contact angle, the trapping efficiency decreases,especially when the angle approaches 90 degrees. The contact angle on aporous aluminum silicate substrate in SC—CO₂ was assumed to be 10 to 40degrees, depending on the confining pressure. The contact angle is givento be 20 to 35° for quartz and 20 to 65° for mica. One complication withcontact angle measurements is that this parameter is sensitive tosurface roughness, and its determination for actual geologic materialscan be challenging.

FIG. 2 illustrates a pore throat 210 and pore body 220 in which aganglion 230 has been trapped. The critical vertical dimension (H_(c))of a SC—CO₂ ganglion that can be trapped is inversely proportional tothe pore diameter, for three different contact angles and at a fixedsize ratio of pore to pore throat. In absence of groundwater flow, fortypical sandstone with a pore diameter from 0.6 to 2 mm, capillarityalone can trap a ganglion with a vertical dimension of 3 to 30 cm.

The effect of reservoir heterogeneity can then be explored by usingEquation (14) to understand the effect of vertical heterogeneity withina reservoir rock on SC—CO₂ entrapment. Consider a horizontal lesspermeable layer (e.g. siltstone) within a permeable sandstone formation.Assume that a SC—CO₂ ganglion is trapped just beneath the finer-grainedinterbed rock. In this case, in order to move upward, the ganglion hasto snap through the pore throats in the interbed at its advancing front,while retreating from the pore bodies in the sandstone at its recedingfront. In other words, the parameter r_(n) in equation (14) now refersto the throat diameter of the interbed, while the parameter r_(p)remains to be the pore size of the sandstone.

FIG. 3 shows how the pore size (or particle size) of the interbedaffects the critical size of a SC—CO₂ ganglion for trapping, assumingthe same pore/throat size ratio for both the sandstone and the interbed.The maximum vertical dimension of the ganglion that an interbed caneffectively immobilize is a direct function of the size of its pores andthe size of the pores of the underlying host formation. For example, fora shale cap rock, capillarity alone can inhibit upward movement of a ˜50meter thick layer of SC—CO₂. A siltstone layer, with a grain size 10times smaller than that of the sandstone, can effectively cap SC—CO₂ganglia (or banks) with vertical dimensions up to 3 m. A siltstone layerwith a grain size 3 times smaller is enough to trap all ganglia withvertical dimensions up to 1 m. Therefore, the vertical heterogeneity ofthe reservoir formation is an important factor for enhancing SC—CO₂entrapment. Numerical simulations indicate that trapping byfiner-grained interbeds may account for up to ˜35% of the total CO₂immobilized. Interbeds here are referred to thin, less continuous layerswith smaller particle sizes. The effectiveness of this mechanism hasbeen demonstrated experimentally. In a CO₂ flooding column experiment,it was found that a thin layer of reduced porosity at the exiting end ofthe column greatly increases (by a factor of 2-5 times) the residual CO₂trapping in the core.

In principle, SC—CO₂ ganglia can form through interface instabilityduring immiscible displacement. In SC—CO₂ injection, the non-wetting CO₂phase displaces the preexisting wetting phase (pore water). Themorphologic instability of the displacement front is described byequations 1-9. A stability analysis of equations 1-9 can be analyzed forwhen a planar interface between the two immiscible liquids advances at aconstant velocity (V_(s)), instability occurs when V_(s) exceeds acritical value V_(s,c) given by:

$\begin{matrix}{V_{s,c} = \frac{{\Delta\rho}\;{gk}\;{\cos(\alpha)}}{\mu_{w} - \mu_{s}}} & (15)\end{matrix}$

where α is the angle between the vertical axis pointing upward and thenormal direction to the interface pointing from SC—CO₂ to water. V_(s,c)can be either positive or negative depending on the interfaceorientation. An unstable front would then become fingered, and thefinger spacing λ is determined by:

$\begin{matrix}{\lambda = {2\sqrt{3\;}{\pi\lbrack \frac{k\;\sigma^{*}}{( {\mu_{w} - \mu_{s}} )( {V_{s} - V_{s,c}} )} \rbrack}^{1/2}}} & (16)\end{matrix}$

Finger spacing predicted with Equation (16) has been shown to agree wellwith numerical simulations.

Now consider a case in which SC—CO₂ is injected to into a horizontalsandstone reservoir. The initial interface between CO₂ and preexistingbrine is vertically aligned (i.e., α=90°). The finger spacing for thefront can be calculated as a function of the velocity of the movingfront and the permeability of the reservoir (FIG. 4). Finger spacingdecreases with both increasing injection rate and decreasingpermeability. For reasonable CO₂ injection rates, the CO₂-waterinterface becomes unstable, and the resulting finger spacing ranges from1 cm to 30 cm. Alternating the injection of CO₂ with water should cutthe fingers horizontally, thus facilitating the formation of isolatedganglia.

Moving ganglia may be understood by considering a vertical cylindricalscCO₂ ganglion in the absence of groundwater flow. From equation (11),the velocity of ganglion rise can be estimated by:

$\begin{matrix}{V_{s}^{g} \approx {\frac{k}{\mu_{w} + \mu_{s}}\lbrack {{{\Delta\rho}\; g} - {\frac{2\sigma\;{\cos(\theta)}}{H}( {\frac{1}{r_{n}} - \frac{1}{r_{p}}} )}} \rbrack}} & (17)\end{matrix}$

In FIG. 5, the velocity of ganglion rise is calculated as a function ofthe vertical dimension (H) of the ganglion. A sufficiently largeganglion will rise, and its velocity will increase with its size.Because of interfacial instability, as described in the previoussection, a large ganglion may experience further fingering at itsadvancing front and break into smaller pieces, causing further trapping.

A ganglion may grow as it moves due to coalescence with other ganglia inthe pathway. However, once it becomes large enough, the ganglion willbreak up through interface instability. This breaking and trappingmechanism thus imposes an important limit on ganglion size evolution. Inthis sense, the mobility of a group of ganglia becomes self-limited.This concept points to a new way for making small ganglia for capillarytrapping, that is, to inject SC—CO₂ into the bottom of the reservoir andthen let it rise. As it rises, a CO₂ bank will automatically break upinto small pieces. Based on a scaling analysis of equations (1-9), thetravel distance required for this breakup is probably on the samemagnitude as the original ganglion size. Note that the terms of “size”and “vertical extension” interchangeably, because we expect that thesurface tension of a ganglion would tend to minimize the aspect ratio ofthe ganglion.

Now consider the mobilization of SC—CO₂ ganglia in a water flow field.As shown in FIG. 6 (solid line), the critical ganglion size formobilization decreases with increasing water flow velocity. Oncemobilized, a ganglion would be carried down along the water streamthrough entrainment. The velocity of a ganglion entrained depends on itssize. Consider a horizontal cylindrical ganglion with its length of Land, for simplicity, ignore the buoyancy term in equation (11). Fromequation (11), the entrainment effect can be described by the velocityratio of ganglion to the carrying fluid:

$\begin{matrix}\begin{matrix}{\frac{V_{s}^{g}}{V_{w}^{0}} = {\frac{\mu_{w}}{\mu_{w} + \mu_{s}} - {{\frac{k}{\mu_{w} + \mu_{s}} \cdot \frac{2\sigma\;{\cos(\theta)}}{{LV}_{w}^{0}}}( {\frac{1}{r_{n}} - \frac{1}{r_{p}}} )}}} \\{= {\frac{\mu_{w}}{\mu_{w} + \mu_{s}} - {{\frac{k}{1 + {\mu_{s}\text{/}\mu_{w}}} \cdot \frac{2}{L\;{Ca}}}( {\frac{1}{r_{n}} - \frac{1}{r_{p}}} )}}}\end{matrix} & (18)\end{matrix}$

where Ca [=μ_(w)V_(w) ⁰/σ cos(θ)] is the capillary number. For a givensize, a ganglion would be entrained only when the carrying flow velocityexceeds a critical value (the intercept of a dash line with the X-axis)(FIG. 6). It seems unlikely for a regional groundwater flow (say, with aflow rate <10⁻⁵ m/s) to mobilize any injected SC—CO₂ once the SC—CO₂phase is broken into small ganglia with a size less than 40 cm. During aCO₂ injection time period, however, due to high flow rates, SC—CO₂ganglia may be carried away by water flows. In a given water flow field,a larger ganglion would move faster than a smaller one. As it moves, alarge ganglion may grow by coalescence with other ganglia in thepathway, and may eventually break up due to interface instability. Themovement of a ganglion can also potentially be affected by the presenceof its neighboring ganglia, leading to a so-called crowding effect.

The model formulated above provides a unified framework to relate thecapillary trapping of SC—CO₂ to key controlling factors such as ganglionsize, surface tension, contact angle, rock pore structure, and thechemistry of phase interfaces. The model analyses demonstrate thatcapillary trapping can be an important mechanism for long-term geologicstorage of CO₂. The analyses show that the movement of a SC—CO₂ ganglionis inversely dependent on its dimension: the smaller the ganglion, themore difficult it is to move. Therefore, breaking the injectedsupercritical CO₂ into small ganglia can significantly enhance theeffectiveness of capillary trapping. A large, mobile ganglion canpotentially break up into smaller, less mobile gangli through theinstability of the CO₂-water interface during buoyant rise, andtherefore the mobility of SC—CO₂ in the subsurface is self-limited. TheSC—CO₂ ganglia can be made through deliberately engineered interfaceinstability of immiscible flows, and their size distribution can becontrolled by SC—CO₂ injection mode and rate.

Ganglion dynamics presented above provides a new perspective formaximizing subsurface CO₂ trapping and safe storage. As shown in FIG. 4,a relatively homogeneous medium with a larger grain size (i.e. highpermeability), which is favored for high reservoir injectivity, wouldresult in larger scCO₂ ganglia due to great permeability. However,larger pores and larger ganglia would reduce the effectiveness ofcapillary trapping, as indicated in FIG. 2. Therefore, there should bean optimal pore size for capillary trapping of SC—CO₂, balancingpermeability and porosity (FIG. 7). The model also shows that thevertical structural heterogeneity of reservoir rock can greatly enhanceCO₂ ganglion trapping (FIG. 3). Therefore, a sandstone formation with amedium grain size and significant vertical heterogeneity may constitutean ideal medium for capillary trapping of SC—CO₂.

The disclosed model presents a complex picture of population dynamics ofSC—CO₂ ganglia in the subsurface. Percolation theory predicts that, neara percolation threshold in immiscible displacement, when the non-wettingliquid starts to become disconnected, the number (p) of ganglia of sizeL follows a power law:p(L)˜L ^(−τ)  (19)

where τ is a constant (=˜2.0). This relationship has been confirmed bydirectly imaging the size distribution of gas bubbles co-injected withwater into sandstone columns. As discussed above, a large ganglion canspontaneously break up during movement. The critical size estimated inFIGS. 2 and 5 thus impose an upper limit on the size distribution ofSC—CO₂ ganglia. The actual distribution may follow a truncated powerlaw. The capacity of a geologic medium for capillary trapping (CCT) canthen be related to the key controlling factors by equation (20):

$\begin{matrix}{{{CT}\; \propto {\int_{r_{p}}^{H_{c}}{{p(L)}\ {\mathbb{d}L}}}} = {\frac{1}{r_{p}} - {\frac{{\Delta\rho}\; g}{2\;{{\sigma cos}(\theta)}}{\frac{r_{p}r_{n}}{r_{p} - r_{n}}.}}}} & (20)\end{matrix}$

This relationship is qualitatively consistent with the measurements ofresidual saturation for SC—CO₂ and n-decane in brine-saturated Bereasandstone. The measurements show a systematically higher residualsaturation for n-decane than that for SC—CO₂. Note that n-decane has arelatively smaller density difference (Δρ) and higher surface tension(a) than SC—CO₂.

The maximum capacity of capillary trapping can be estimated by assumingthat it corresponds to the percolation threshold, at which thenon-wetting phase just becomes disconnected. The percolation thresholddepends on the shape and the size uniformity of ganglia. Based on asimple cubic lattice calculation, the threshold is estimated to be 0.341for ganglia with a uniform size. This is consistent with a recent columnexperiment, which shows that the maximum residual supercritical CO₂phase in Berea sandstone is about 35%. This seems reasonable,considering that the core sample used in this experiment is small (˜4 cmin diameter and 8 cm in length) and, as a result, the size distributionof ganglia is limited to a relatively narrow range. In an actualreservoir, however, the size of ganglia is expected to distribute over amuch broader range, and the actual capacity could be higher. As pointedout earlier, one advantage of capillary trapping is that this mechanismdoes not require a cap rock or the structural integrity of cap rock.Therefore, the total capacity of sequestration by capillary trapping ona regional scale could be significant.

As discussed above, the key parameters controlling capillary trapping ofSC—CO₂ include: the surface tension, the contact angle, the densitydifference between SC—CO₂ and pore water, and the pore structure of themedia. There are large uncertainties associated with each of theseparameters. First, contact angles for many reservoir-relevant mineralsare poorly known for the potential range of reservoir pressure,temperature, and chemical conditions. Furthermore, contact angles canpotentially be modified by the presence and properties of water films onmineral surfaces. The thickness of water film is controlled by mineralsurface properties and pore-water chemistry.

Surface tension between SC—CO₂ and aqueous solution can potentially beaffected by solution chemistry and possible organic compound dissolutioninto either the supercritical phase or the aqueous solution, which maymodify the interfacial properties between the two liquids. As indicatedin equation (7), the macroscopic effective surface tension σ* isscale-dependent, which makes it difficult to characterize for an actualsystem. In general, chemical reactions will be enhanced by the formationof SC—CO₂ ganglia due to an increase in specific surface area of SC—CO₂.The key parameters identified here may then evolve with time. Forexample, dissolution of organics (e.g. oil residues) from mineralsurfaces can change the wetting properties of the surface and thereforethe liquid-mineral contact angle. Mineral dissolution and precipitationmay change the pore structure of the storage media. For example,secondary mineral precipitation may enhance capillary trapping byreducing porosity or pore throat size specifically. As minerals dissolveand new minerals precipitate, the pore surface properties (e.g., surfaceroughness and chemical identity) will also change. Evaluating theimportance of these effects on long-term CO₂ trapping is scientificallychallenging.

The analysis presented here indicates that the size of SC—CO₂ gangliamay distribute over a wide range following a power law and the size oflarge ganglia may exceed the size of what is generally considered to bea representative element volume. More importantly, this disclosedmethodology shows that the size of a ganglion is one of the mostimportant factors controlling capillarity trapping of SC—CO₂ ganglia.None of the existing continuum models explicitly account for theimportant effect of ganglion size.

The ganglion concept developed above also provides a reasonableexplanation for seemingly contradictory observations on residual gassaturation in a porous medium. With an X-ray computer tomography (CT)technique, Suekane et al. imaged the distribution of nitrogen gasbubbles in Berea and Tako sandstone in a core-flooding experiment. Theyfound that, on a local scale (˜1 mm), the residual gas saturationincreases with an increase in porosity. However, on a core scale, theresidual gas saturation exhibits an inverse relationship with porosity.These seemingly contradictory observations are actually the twodifferent manifestations of the same immiscible displacement process.Based on the earlier discussions, a non-wetting fluid tends to occupylarge pore spaces as much as possible to minimize gas-water interfacialenergy. Therefore, on a scale close to pore size, the residual gassaturation should positively correlate with local porosity. However, ona bulk scale, because of the same tendency to minimize gas-waterinterfacial energy, smaller pores (actually smaller pore throats forthis matter) would create more capillary resistance for gas bubbles tosnap through pore necks, thus promoting residual trapping. Thus, on acore scale, the residual gas saturation should to be inverselycorrelated with porosity (i.e., pore size), as indicated in equations(14) and (18).

Finally, the concept developed here allows for the development of a newtechnique for characterizing and monitoring SC—CO₂ in subsurfaceenvironments. For example, recent interest in using acoustic waves toenhance oil recovery has stimulated a significant amount of work on theinteraction of acoustic waves with non-wetting oil blobs in porousmedia. It has been found that acoustic waves may induce capillaryresonance of the blobs and the size of the blob (L) can be related tothe resonant frequency (ω) by:

$\begin{matrix}{L = \frac{16\;{{{\sigma sin}(\theta)}\lbrack {1 + {\sin(\theta)}} \rbrack}^{2}}{{\rho_{s}( {r_{n} + r_{p}} )}^{2}\omega^{2}}} & (21)\end{matrix}$

As discussed above, supercritical CO₂ injected into a reservoir islikely to form discontinuous ganglia. It is reasonable to expect thatacoustic wave attenuation at a specific wave frequency is mainlyattributed to the capillary resonance of ganglia of the appropriatesize. If this is true, then measuring the attenuation of acoustic wavesat various frequencies may allow us to estimate the size distribution ofSC—CO₂ ganglia in subsurface systems.

According to another embodiment of the disclosure, a method for storingCO₂ is disclosed. In this embodiment, SC—CO₂ is alternately injectedwith a fluid. The fluid may be brine, water, or other similar fluid.

FIG. 8 illustrates an exemplary embodiment of this process. As can beseen in FIG. 8, a fluid stream 810 is introduced into a well 815 andinjected into a geologic formation 820. The well 815 may be a verticalwell 815 A or a horizontal well 815B. In another embodiment, the well815 may be oriented at any angle between vertical and horizontal. Thegeologic formation 820 may be sandstone or other porous rock layer. Thegeologic formation may or may not be covered or partially covered with aimpervious cap rock such as shale.

The fluid stream 810 includes alternating amounts, zones or plugs of aliquid and SC—CO₂ to create horizontal spaced zones or plugs of SC—CO₂830 and fluid 840. The SC—CO₂ 830 may be mixed with another fluid beforebeing introduced to the well, such as, but not limited to brine orwater. The fluid 840 may be brine or water. The zones of SC—CO₂ 830 andfluid 840 may include zones of SC—CO₂ 830A and fluid 840B that havepercolated upward.

In an embodiment, the width of the zones of SC—CO₂ 830 and fluid 840 aresufficient to move the previous zone within the formation 820. The widthor thickness of the zones is the distance between the leading andtrailing edge in the zone movement direction. The amount of SC—CO₂ 830and fluid 840 sufficient to move the previously introduced zone withinthe formation 820, and is dependent upon the formation porosity andchemistry. As discussed above, the movement of the SC—CO₂ zones breaksup SC—CO₂ ganglia, reducing the size of the SC—CO₂ ganglia, therebyimproving immobilization. In an embodiment, the thickness of the zonesof SC—CO₂ 830 and fluid 840 are between 1 and 10 meters.

In another embodiment, the amount of SC—CO₂ 830 and/or fluid 840 isselected to allow the zones of SC—CO₂ 830 and fluid 840 to mix withinthe formation as they travel away from the well, the fluid 840 pushingthe SC—CO₂ 830, breaking up the SC—CO₂ ganglia thereby improvingimmobilization. As understood by one in the art, the miscibility ofSC—CO₂ 830 and fluid 840 is small and thus mixing, as understood in thelight of this disclosure, is substantially forming a two phase mixtureof SC—CO₂ 830 and fluid 840. In another embodiment, the SC—CO₂ 830 andfluid 840 are mixed to form a two phase mixture before being introducedinto the well 815.

In another embodiment, the geologic formation 820 is characterized forits vertical variability of pore size and permeability using geophysicaland petrographic methods. An optimal site for CO₂ sequestration would bethe formation with significant vertical pore size/porosity variations(i.e. with interbeds) ranging from 4 μm to 1 mm.

In another embodiment, geophysical methods such acoustic waves andseismic waves can be used to detect or monitor the size distribution ofSC—CO₂ ganglia during or after injection, as indicted by equation 21.

FIG. 10 is a flow chart illustrating an exemplary embodiment of a methodof predicting long term risk of storing CO₂ in a geologic formationaccording to the present invention. As can be seen in FIG. 10, step 1(1010) is site characterization, which includes porosity, pore size, andpore structure, lithology (such as sandstone or carbonate formations)and interbed distribution within the host rock. Interbeds are thin,continuous or discontinuous sediment seams less permeable than the bulkrock formation.

Step 2 (1020) is pore-fluid chemistry, such as but not limited todensity, pH, dissolved salt concentration, and surface tension betweenpore fluid and Sc—CO₂.

Step 3 (1030) is estimating SC—CO₂ ganglion size. Ganglion size isestimated for entrapment for a given groundwater velocity. Ganglion sizemay be determined by Equation 12 above. The ganglia entrapment criteriaare that the ganglion size must be small enough for the capillary forceexerting on the ganglion to counter the buoyancy and the regional flowforce

Step 4A (1040) calculates injection rate and time intervals foralternating SC—CO₂ and fluid injections using equations 15-16.

Step 4B (1050) determines the vertical distance needed for ganglionformation from buoyancy using Equation 17. This step is optional and maybe omitted if no vertical movement is considered.

Step 5 (1060) is SC—CO2 injection according to an injection strategy(e.g., alternating SC—CO2 injection or ganglion formation by buoyancyrising) designed at steps 3 and 4.

Step 6 (1070) uses geophysical detection and monitoring of ganglion sizedistribution, for example, using acoustic wave attenuation caused by thecapillary resonance of SC—CO₂, ganglia to confirm that the ganglion sizedistribution predicted by Equation 6 is the size that immobilizes theganglia. Step 6 is optional.

Step 7 (1080) is determining the long-term risk by analysis of themobility and long-term stability of SC—CO₂ ganglia in subsurface usingganglion entrapment criteria (Equation 12).

It should be appreciated that measurements or determinations may bebased on field measurements, lab measurements, approximations and/orestimates.

Although the invention has been described in detail with particularreference to these preferred embodiments, other embodiments can achievethe same results. Variations and modifications of the present inventionwill be obvious to those skilled in the art and it is intended to coverin the appended claims all such modifications and equivalents. Theentire disclosures of all references, applications, patents, andpublications cited above are hereby incorporated by reference.

What is claimed is:
 1. A method for injecting supercritical-carbondioxide into a geologic formation, comprising: characterizing thegeologic formation; determining the surface tension between fluid of thegeologic site and supercritical carbon dioxide; determiningsupercritical carbon dioxide ganglion size for entrapment for a givenfluid velocity; determining the maximum supercritical carbon dioxideganglion formation by induced viscous interface instability; anddetermining the travel distance of supercritical carbon dioxide ganglionwithin the geologic formation based on entrapment criteria; using thedetermined travel distance to determine risk of supercritical carbondioxide escaping from the geologic formation; and injectingsupercritical carbon dioxide into the geologic formation.
 2. The methodof claim 1, further comprising: determining the vertical distance neededfor supercritical carbon dioxide ganglion formation.
 3. The method ofclaim 1, wherein the maximum supercritical carbon dioxide formation isdetermined by determining the point of induced viscous interfaceinstability.
 4. The method of claim 1, wherein supercritical-carbondioxide and a fluid are alternately injected into the geologicformation.
 5. The method of claim 1, wherein the supercritical-carbondioxide and a fluid are mixed prior to being injected into the geologicformation.
 6. The method of claim 1, further comprising: usinggeophysical detection to confirm ganglion size distribution.
 7. A methodof injecting CO2 into a geologic formation, comprising: characterizingthe geologic formation; determining the surface tension between fluid ofthe geologic site and supercritical carbon dioxide; determiningsupercritical carbon dioxide ganglion size for entrapment for a givenfluid velocity; determining the maximum supercritical carbon dioxideganglion formation by induced viscous interface instability; determiningthe travel distance of supercritical carbon dioxide ganglion within thegeologic formation based on entrapment criteria: and determining therisk based on supercritical carbon dioxide ganglion entrapment criteria;and injecting supercritical carbon dioxide into the geologic formation.8. The method of claim 7, further comprising: determining the verticaldistance needed for supercritical carbon dioxide ganglion formation.